I was interested in validating or invalidating the mach 4 number. I guess it depends on the specific rocket, but the 122 mm M-21OF-M Rocket, sometimes referred to as Katyusha (although that was the name of a specific launcher, not the rocket [0]) is 660 m/s or about mach 2 [1].
0. https://en.wikipedia.org/wiki/Katyusha_rocket_launcher
1. https://kintex.bg/product-4-77